Cairo , Egypt -LRB- CNN -RRB- -- `` Freedom ! ''

That word , yelled out in Arabic , reverberated Friday along the banks of the Nile River in Cairo -- as well as in the port city of Alexandria , near the canal in Suez , and other pockets of Egypt . Many demonstrators voicing their desire for a new government and new political future remained on the streets well into Saturday morning , defying a curfew and revelling in a historic day in a nation whose history dates back millennia .

By early Saturday , police were nowhere to be seen in the capital of Cairo , with military forces deployed on streets all around the nation for the first time in more than three decades . They were ordered out by President Hosni Mubarak , whom many demonstrators were urging to step down or , at least , institute dramatic economic and political reforms .

`` We want -LRB- Mubarek -RRB- to leave , '' said Ahmed , whose last name was withheld to protect his identity . `` His time is over , '' the 19-year-old law student said early Saturday from Raml Square in central Alexandria .

Mubarak has been in power for 30 years , during which time Egypt has established itself as one of the most important powers in the region and a strong ally of the United States . At the same time , the long-time ruler and his regime had a reputation for restricting freedoms and staunchly holding onto power .

Resistance in the past had often been stifled by either political manuevering or the police , members of which were out in full force this week . But rarely have they met an opposition force as large , or as apparently determined .

`` Police have always been violent , but we have n't seen it this way , '' Sarah Sirgany , a reporter for Daily News Egypt who has been posting regular developments on Twitter , told CNN 's Piers Morgan . `` We have n't seen this many people on the streets at the same time . ''

Video footage from Friday showed throngs of protesters charging down a bridge over the Nile River in Cairo , overrunning police trucks that fired off tear gas with minimal effect . Elsewhere , demonstrators torched and ransacked the headquarters of Mubarak 's ruling National Democratic Party .

When protesters circled the Ministry of Information in Cairo on Friday , they were greeted by police , who responded with sharp cracks of gunfire .

It 's not clear whether police shot at protesters or into the air , whether their bullets were rubber or steel , whether anyone was wounded or killed .

There were many other reports of run-ins , and the U.N. High Commissioner for Human Rights reporting early Friday that the government had arrested more than 1,000 people , including political opposition leader Mohamed ElBaradei .

Mohammed Mansour , a resident of the Shubra neighborhood of Cairo , said that he and fellow demonstrators had been `` beaten and assaulted by police '' since Monday , when the popular unrest began .

Continuing to fight Friday , he said that his group had beaten back police , who retreated . Later he claimed , protesters set fire to three police stations and about 20 police cars .

`` We went out today and we were ready to die , so our children can live in dignity , '' said Mansour .

Protesters ' interactions with Egypt 's military -- members of an army that is widely respected in Egypt -- were far more friendly . In Cairo and Alexandria , many protesters greeted troops with embraces and cheers , some even shaking hands with soldiers .

Mansour , the Cairo resident , said he and fellow demonstrators celebrated when they saw troops roll into town , and they were not alone .

`` It means we are victorious , '' he said . `` If the army comes out , that means the government ... is no longer in control . ''

In the wee hours of Saturday , with the curfew ostensibly in effect , people continued to come up to friendly army troops , greeting them and posing for pictures by tanks . Some military personnel were stationed outside burned out police stations , but did little to prevent people from going into them and coming out with chairs , tables and various valuables .

The army was n't the only side exercising restraint .

The Muslim Brotherhood sent its followers onto the streets after Friday prayers , the first time Egypt 's large and venerable -- but illegal -- Islamic opposition called for protest during this round of demonstrations .

And when younger Muslim Brotherhood protesters seemed ready to hurl rocks at the police in Alexandria , Egypt 's second-largest city , older men put their arms around their shoulders , calming them down .

Just after midnight Saturday , Mubarak gave a speech defending and explaining the government 's response to the protests while saying that he 'd soon form a new government mindful of the demonstrators ' demands for policy changes .

Still that did n't appease many on the streets , who vowed to continue demonstrating again against what they felt was an unjust ruling government that needed a fresh start -- without Mubarak .

`` We are one of the richest Arab countries , and we want to live , '' said a 20-year-old student named Mohammed , whose last name was withheld to protect his identity , from Alexandria . `` Let a new government form , but if we do n't get what we ask for , we will go back to the streets again and again . ''

Another protester in Alexandria , an 18-year-old taxi driver named Yousef , did n't even think the entrenched Egyptian ruler deserved even that much of a chance . He said Egyptians should press on with their protests , following the lead of their fellow African nation Tunisia .

There , President Zine El Abidine Ben Ali left the country after 23 years in power following weeks of demonstrations against his rule . The new government , under Prime Minister Mohamed Ghannouchi , announced new freedoms and promised to institute numerous democratic-minded reforms .

`` They kept protesting until he fled the country , '' Yousef said of Tunisia . `` We will do more and more , we will continue our demonstrations , and we will do 3,000 times more of what the Tunisians did . ''

CNN 's Salma Abdelaziz , Saad Abedine , Ben Wedeman in Cairo and Nic Robertson in Alexandria contributed to this report .

@highlight

NEW : A protester in Alexandria says President Mubarak 's `` time is over ''

@highlight

NEW : Video footage shows demonstrators overruning police on a Nile River bridge

@highlight

NEW : A protester in Cairo says : `` We 'll do 3,000 more than what the Tunisians did ''

@highlight

Protesters greet military troops on the streets with hugs and handshakes